A problem frequently encountered in (full duplex) digital data communication systems that employ a limited bandwidth channel is the presence of linear distortion introduced into the signal propagation path, which may manifest itself as intersymbol interference (ISI) in the received symbol sequence. In order to reduce the effects of this distortion, it is common practice to process the received signals by some form of transversal filter mechanism, such as a decision feedback (DFB) equalizer, an `ideal` classical example of which is diagrammatically illustrated in FIG. 1.
As shown in FIG. 1, the front end of the DFB equalizer, to which the received symbol (plus noise) stream is applied, typically contains a noise-whitening filter 7 which is operative to "whiten" the noise spectrum present in the incoming signal sequence and to reshape the received signal. This filtered signal is then applied to an analog matched filter 8 that is matched to the reshaped signal spectrum. By `matched` filter is meant that the signal is sampled (T) once per symbol, at an optimum sampling time.
The samples are then fed to a T-spaced feedforward linear filter section 11. T-spaced feedforward linear filter comprises a delay line 12, each z.sup.-1 stage of which stores a respective symbol sample. The contents of the respective stages of the delay line are multiplied in multipliers 13 by respective weighting coefficients W.sub.i and then summed in adder 14, to produce a combined output for application to a downstream decision feedback section 15, from which output data decisions are derived on output link 17.
Specifically, the output of adder 14 is adjusted at 16 by subtracting the output of decision feedback section 15 from the output of adder 14. The effect of subtracting the output of the decision feedback section 15 from the linear filtered section 11 is to remove intersymbol interference due to previously detected symbols. Data decision estimates are derived on a symbol by symbol basis, by means of a symbol decision mechanism, such as a symbol slicer 18. Symbol slicer 18 slices the signal at levels equally spaced between reference levels for received symbols. These output data decisions are then fed back to a linear delay line 21 to remove intersymbol interference from future symbols. Like delay line 12, the contents of the respective z.sup.-1 stages of delay line 21 are multiplied in multipliers 23 by respective weighting coefficients and then summed in an adder 24 to produce a combined output to be subtracted from the output of feedforward section 11.
A residual error signal (not shown) for adjusting the weighting coefficients of the linear section 11 and the decision feedback section 15 of the filter may be obtained by differentially combining data decision estimates at the output 17 with the output of summation block 16.
In the ideal conventional DFB equalizer architecture of FIG. 1, the weighting coefficients W.sub.i for the feedforward filter section 11 are assumed to be one-sided or "anticausal" and the last, or most delayed, tap z.sup.-1 of delay line 12 is typically the largest,.and is commonly referred to as the `main` tap, the `reference` tap, or the `cursor` tap. The current decision on the value of a received symbol is customarily considered to have its dominant energy contribution derived through this tap. The weighting taps of the feedback section 15.take on values equal to samples of the postcursor or `tail` of the received symbol which follows as the symbol energy decays.
Because the classical DFB structure assumes that the number of taps or stages is infinite, practical realization requires truncating the lengths of the respective feedforward and feedback delay lines at some practical number of taps per filter. In order to prevent significant degradation of the signal, the number of taps selected for the feedback stage 15 must be sufficient to span all significant samples of the signal at the point of ISI cancellation. The number of taps of the upstream stage 11 is not as readily apparent. Although this number is related to the precursors, it is not necessarily equal to the significant energy span of the precursors.
one method to establish the length of the filter is to either compute the coefficients or simulate the filter with a large number of coefficients and determine how many are significant. However, this approach is heavily channel dependent. Since, in practice, the signal processing circuit designer does not have the freedom to implement a "whitened" matched filter in the analog domain prior to sampling, which would be different for every line shape and noise spectrum, some prescribed fixed shaped is employed, or a simple anti-aliasing filter may be used upstream of the sampling point.
FIG. 2 diagrammatically illustrates an example of a practical implementation of the above described classical DFB equalizer structure, in which the linear feedforward section 11 has a finite number M of delay line stages z.sup.- and feedback section 15 has a finite number N of delay line stages z.sup.-1. The received symbol sequence (and any accompanying noise) is filtered in a fixed analog filter 31, which is operative to band-limit the signal prior to sampling at 32. The shape of filter 31 may be such that it rolls off and partially whitens the noise component; it is normally not adaptive and cannot behave as a matched filter because the channel characteristics are unknown. A matched filter must have a prescribed amplitude and phase characteristic, and its implementation may be complex particularly in the analog domain for an arbitrary channel shape, even if such shape were known.
In order to train the adaptive equalizer, data values or symbols corresponding to the transmitted data are used. Training is normally carried out using a predetermined training sequence. Alternatively, if the data decisions are sufficiently reliable prior to convergence, these data decisions can be used for training. When a training sequence is employed it is common practice to derive a rough approximation of the amount of delay and allow the taps to grow until the largest tap is identified. Then the amount of delay is adjusted so as to place the cursor tap at the desired location which, as noted above, is the last stage of the feedforward delay line 12.
An alternative approach to implementing the `classic` DFB equalizer of FIG. 1, diagrammatically illustrated in FIG. 3, involves a `brute force` modification of the front end filtering structure associated with feedforward section 11. If sufficient information is known about the dispersive channel and noise content of the received signal, an adaptive whitened matched filter may be employed. In the environment of HDSL signals, the spectrum of the noise is often assumed to be known, and signal energy essentially vanishes above the Nyquist frequency, particularly on long lines. Given this information, a `fixed` noise-whitening filter mechanism, shown at 35 in FIG. 3, may be inserted in the feedforward signal flow path, downstream of the sampling point.
The sampling rate may be one sample per symbol time (T-spaced sampling), since for long loops there is very little signal energy received at the upper edge of the band. It may be inferred that only a small amount of signal energy will be aliased from the range of frequencies greater than half the symbol rate. If so, and the "folded" spectrum consists essentially of only the original frequency component prior to folding (sampling), then an adaptive matched filter may be reasonably well synthesized after sampling. An analog matched filter is capable of operating on the entire frequency spectrum prior to folding; however, if there is no energy above the Nyquist sampling rate available at the receiver to fold or to be utilized during detection, then the matched filter may be more readily implemented as a digital filter downstream of sampling, as shown at 37. It should be observed, however, that noise is present at the higher frequencies. As a consequence, to limit noise, a well behaved anti-aliasing filter 39 is required. In the filter architecture of FIG. 3, the fixed noise-whitening filter 35 need not be adaptive if the input noise shape is well defined, such as is the case for current Bellcore standards.
As noted above, the output of noise-whitening filter 35 is coupled to adaptive matched filter 37, which is matched to the signal after whitening; and the filtered signal is then applied to the feedforward stage of the DFB equalizer. The length of the linear filter 12 in the feedforward section 11 will depend upon how many taps are required to eliminate all the (substantial) precursor content that has been injected into the signal by the matched filter. Since an accurate matched filter will generate precursors as long as the postcursors, which is on the order of a hundred or so samples for long HDSL loops, even prior to matched filtering, it can be expected that a long feedforward filter will be required.
Unfortunately, in the alternative filter architecture of FIG. 3, the addition of noise-whitening filter 35 and adaptive matched filter 37 (the length of which must be on the order of the tails or postcursors of the received symbols), and the considerable length of feedforward filter stage 11 creates a complex digital implementation problem.